Verify Green's Theorem for Jo where C' is a triangle with vertices (0,0), (1, 3), and (1,5) traced out counter-clockwise by (a) computing the line integral directly and (b) using Green's Theorem to compute the integral. (6y-3y² + x) dx + yx³ dy

Q: Green’s Theorem for line integrals Use either form of Green’sTheorem to evaluate the following line…

A: By Green's Theorem, we have where R is the region enclosed by curve C.

Q: Calculate the line integral F. dr, where F (3y, -3z, 2x + 2) and C' is the boundary of a triangle…

A: We will find line integral by using stokes theorem .

Q: Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise (6x…

A: Greens theorem:∫CPdx+Qdy=∫∫R∂Q∂x-∂P∂ydxdy, where R is the region bounded by the simple closed curve…

Q: 3) Consider (a) Calculate the line integrals F(x, y, z) = −7+ (²²₂2) 5+ yzk 2 [ F(7) - dr Ja along…

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Q: Evaluate the complex integral cx+yi [*** az (eb₂²+c) dz if a = 4.8, b = 0.7, c = 3, v = 3, x = 1 and…

A: Given : a=4.8 , b=0.7, c=3, v=3,x=1 and y=4 To find : ∫vx+yiazebz2+cdz

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

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Q: Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented…

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Q: Consider the line integral xy dx + xy° dy with C the triangle with vertices (0, 0). (1,0), and (1,…

A: Given, the line integral Where C is the triangle with vertices.

Q: cV4-x² Rewrite the integral (3) x – y dz dy dx in spherical coordi- -x² -y? nates. Do NỘT evaluate…

A: We are given a triple integral ∫-22∫04-x2∫-4-x2-y20 x-y dzdydx whose coordinates are x, y, z. We…

Q: I don't understand why R0=C2+C3lnr

A: Please check step 2 for the solution.

Q: Find the value of 1-1/16 (x² + y²) dy dx + ſ', [~ ² * (x² + y²) dy de by expressing it as one…

A: From, the given integral, draw the region of integration.

Q: Q.2: Let C be the line joining A(-1,0), B(0,1), D(1,1), and E(2,0). Evaluate: Scy dz tor and radius…

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Q: Consider the following line integral. fxy dx + x²y³ xy dx + x²y³ dy, C is counterclockwise around…

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Q: Evaluate the line integral (2x - y + 5)dx + (5y + 3x - 6)dy, for which the path C C traverses around…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O…

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Q: Jo F dr, where F = (3-2y, x-1, -2z) and C is the boundary of a triangle with vertices (0, 0, -3),…

A: Given F=3-2y, x-1, -2z C is the boundary of a triangle with vertices (0, 0, -3), (0, 4, 5), (2, 0,…